If $a$,$b$,$c \in {R^ + }$ are such that $2a$,$b$ and $4c$ are in $A$.$P$ and $c$,$a$ and $b$ are in $G$.$P$., then

  • A

    $a^2$, $ac$ and $c^2$ are in $A$.$P$.

  • B

    $c$, $a$ and $a$ + $2c$ are in $A$.$P$.

  • C

    $c$, $a$ and $a$ + $2c$ are in $G$.$P$.

  • D

    $\frac{a}{2}$,$c$ and $c$ -a are in $G$.$P$.

Similar Questions

The first two terms of a geometric progression add up to $12.$ the sum of the third and the fourth terms is $48.$ If the terms of the geometric progression are alternately positive and negative, then the first term is

  • [AIEEE 2008]

Let $n \geq 3$ and let $C_1, C_2, \ldots, C_n$, be circles with radii $r_1, r_2, \ldots, r_n$, respectively. Assume that $C_i$ and $C_{i+1}$ touch externally for $1 \leq i \leq n-1$. It is also given that the $X$-axis and the line $y=2 \sqrt{2} x+10$ are tangential to each of the circles. Then, $r_1, r_2, \ldots, r_n$ are in

  • [KVPY 2014]

The greatest integer less than or equal to the sum of first $100$ terms of the sequence $\frac{1}{3}, \frac{5}{9}, \frac{19}{27}, \frac{65}{81}, \ldots \ldots$ is equal to

  • [JEE MAIN 2022]

The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$, will be

If the sum of three terms of $G.P.$ is $19$ and product is $216$, then the common ratio of the series is